However, the more complex a scenario becomes, the more challenging it is to define admissible parameters, e.g. positive definite variance-covariance matrices.
The bivariate hazard model is λ T,ijk (t ; x ijk ) = λ T0 (t ) exp (x ijk β Ti + e Tij ) and λ D,ijk (d ; x ijk ) = λ D0 (d ) exp (x ijk β Di + e Dij ) where the [eTij eDij]'s are independent and identically distributed according to a bivariate normal distribution with null mean vector and positive-definite variance matrix.
The problem studied in the paper concerns the estimation of individual weights of p objects according to the model of an A-optimal chemical balance weighing design with a positive definite diagonal variance matrix of errors under the restriction p1+p2= q⩽p, where p1 and p2 represent the numbers of objects placed on the left and on the right pan, respectively, in each of the measurement operations.
It should be noted that G is an n by d matrix of random effects with G ~ MVN n × d (0, K, V g ) where V g is a d by d symmetric positive definite matrix of genetic variance component, and E is an n by d matrix of residual errors with E ~ MVN n × d (0, I, V e ) where V e is a d by d symmetric positive definite matrix of residual variance component (K and I are the same in the two models).
Second, due to the positive semi-definite structure of error variance, multiple-threshold strategies cannot outperform single-threshold strategies in terms of prediction error variance given that both single- and multiple-threshold strategies are of the same mathematical structure such as both being linear or non-linear and so on.
Not definitive, just definite.
When either macro or micro-environmental sensitivity was simulated (Table 7), the variance-covariance structures were forced to be positive definite in many replicates, due to estimates of variances at the boundary.
But the difference is too minor to make any definite statements, as also shown by the variance of the estimates.
